Size of a tarball without untarring - Catch parent tar ball has sub tars

hi,
I am in a weird situation. I have a parent tarball which contains 2 sub tarballs.
The structure is such :
Parent.tar.gz ---- > child1.tar.gz and child2.tar.gz
I need to get the size of the parent tarball without untaring it

I know that the command is

gunzip -c  parent.tar.gz | wc -c 

However this gives me the sizeof parent tarball with the compressed size of the child tarballs. When I actually check the size of child1.tar.gz with the same command its much bigger than the size returned for the parent.tar.gz with the same command.

Can someone guide me as to how to check recuirsivly for the total size of a tar ball ?

There is nothing very odd about the results you describe. If you take 3 files each one megabyte of text and tar them into child.tar you have a roughly 3 megabyte tar file. Now you compress it and get, say a 25 kilobyte child.tar.gz. Now you create a parent.tar which is about 25 kb. If you ry to compress data which is mostly compressed, it won't compress much if at all. So now maybe parent.tar.gz is 24 kb. This is exactly the situation that you disbelieve. parent.tar.gz will expand back to 25 kb. But the child.tar.gz inside it will expand back to 3 MB.